1594520617

# Can You Remove 99% of a Neural Network without Losing Accuracy?

Even the most common neural network architectures have a lot of parameters. ResNet50, which is a frequently used baseline model, has ~25 million. This means that during training, we perform a search in a 25 million dimensional parameter space.

To put this number in perspective, let’s take a look at a cube in this space. An n-dimensional cube has 2ⁿ vertices, so in 25 million dimensions, we are talking about 2²⁵⁰⁰⁰⁰⁰⁰ points. In a search grid, this would be just a single element. For comparison, the number of atoms in the observable universe is estimated to be around 10⁸². It is safe to say that the magnitude of this problem is incomprehensible to us humans.

Thus, reducing the number of parameters would have several benefits. A sparse network is not only smaller, it is faster to train and use. Where hardware is limited, such as in embedded devices or smartphones, speed and size can make or break a model. In addition, more complex models are more prone to overfitting. So, restricting the search space also acts as a regularizer.

However, this is not a simple task, as reducing the model’s capacity can also lead to loss in accuracy. Thus, there is a delicate balance between complexity and performance. In this post, we are going to take a deeper look into what the challenges and potential solutions are.

Weight pruning

To start off, the simplest problem would be to aim for reducing model parameters after training. This would not help with the training itself, but would reduce computational requirements for inference.

The process of eliminating weights is called pruning. (I will use weights and parameters interchangeable from now.) Its origins go back to the famous paper Optimal Brain Damage by Yann LeCun, John S. Denker and Sara A. Solla._ (If you know an earlier reference, feel free to leave a comment!)_

They proposed the following iterative pruning method.

1. Train the model.
2. Estimate the saliency of each weight, which they define by the change in the loss function upon perturbing the weight. The smaller the change, the less effect the weight has on the training.
3. Remove weights with the lowest saliency. (That is, set their value to zero and keep it there for the rest of the process.)
4. Go to Step 1. and retrain the pruned model.

Continuing the training with pruned weights is necessary. The authors observed that without it, the objective function (a.k.a. the loss) increases significantly when a large portion of the weights are removed.

One particular challenge arises with this method when the pruned network is retrained. It turned out that due to its decreased capacity, retraining was much more difficult. The solution to this problem arrived later, along with the so-called Lottery Ticket Hypothesis, which put this problem into a whole another perspective.

#data-science #artificial-intelligence #neural-networks #deep-learning #machine-learning

1594520617

## Can You Remove 99% of a Neural Network without Losing Accuracy?

Even the most common neural network architectures have a lot of parameters. ResNet50, which is a frequently used baseline model, has ~25 million. This means that during training, we perform a search in a 25 million dimensional parameter space.

To put this number in perspective, let’s take a look at a cube in this space. An n-dimensional cube has 2ⁿ vertices, so in 25 million dimensions, we are talking about 2²⁵⁰⁰⁰⁰⁰⁰ points. In a search grid, this would be just a single element. For comparison, the number of atoms in the observable universe is estimated to be around 10⁸². It is safe to say that the magnitude of this problem is incomprehensible to us humans.

Thus, reducing the number of parameters would have several benefits. A sparse network is not only smaller, it is faster to train and use. Where hardware is limited, such as in embedded devices or smartphones, speed and size can make or break a model. In addition, more complex models are more prone to overfitting. So, restricting the search space also acts as a regularizer.

However, this is not a simple task, as reducing the model’s capacity can also lead to loss in accuracy. Thus, there is a delicate balance between complexity and performance. In this post, we are going to take a deeper look into what the challenges and potential solutions are.

Weight pruning

To start off, the simplest problem would be to aim for reducing model parameters after training. This would not help with the training itself, but would reduce computational requirements for inference.

The process of eliminating weights is called pruning. (I will use weights and parameters interchangeable from now.) Its origins go back to the famous paper Optimal Brain Damage by Yann LeCun, John S. Denker and Sara A. Solla._ (If you know an earlier reference, feel free to leave a comment!)_

They proposed the following iterative pruning method.

1. Train the model.
2. Estimate the saliency of each weight, which they define by the change in the loss function upon perturbing the weight. The smaller the change, the less effect the weight has on the training.
3. Remove weights with the lowest saliency. (That is, set their value to zero and keep it there for the rest of the process.)
4. Go to Step 1. and retrain the pruned model.

Continuing the training with pruned weights is necessary. The authors observed that without it, the objective function (a.k.a. the loss) increases significantly when a large portion of the weights are removed.

One particular challenge arises with this method when the pruned network is retrained. It turned out that due to its decreased capacity, retraining was much more difficult. The solution to this problem arrived later, along with the so-called Lottery Ticket Hypothesis, which put this problem into a whole another perspective.

#data-science #artificial-intelligence #neural-networks #deep-learning #machine-learning

1623135499

## No Code introduction to Neural Networks

### The simple architecture explained

Neural networks have been around for a long time, being developed in the 1960s as a way to simulate neural activity for the development of artificial intelligence systems. However, since then they have developed into a useful analytical tool often used in replace of, or in conjunction with, standard statistical models such as regression or classification as they can be used to predict or more a specific output. The main difference, and advantage, in this regard is that neural networks make no initial assumptions as to the form of the relationship or distribution that underlies the data, meaning they can be more flexible and capture non-standard and non-linear relationships between input and output variables, making them incredibly valuable in todays data rich environment.

In this sense, their use has took over the past decade or so, with the fall in costs and increase in ability of general computing power, the rise of large datasets allowing these models to be trained, and the development of frameworks such as TensforFlow and Keras that have allowed people with sufficient hardware (in some cases this is no longer even an requirement through cloud computing), the correct data and an understanding of a given coding language to implement them. This article therefore seeks to be provide a no code introduction to their architecture and how they work so that their implementation and benefits can be better understood.

Firstly, the way these models work is that there is an input layer, one or more hidden layers and an output layer, each of which are connected by layers of synaptic weights¹. The input layer (X) is used to take in scaled values of the input, usually within a standardised range of 0–1. The hidden layers (Z) are then used to define the relationship between the input and output using weights and activation functions. The output layer (Y) then transforms the results from the hidden layers into the predicted values, often also scaled to be within 0–1. The synaptic weights (W) connecting these layers are used in model training to determine the weights assigned to each input and prediction in order to get the best model fit. Visually, this is represented as:

#machine-learning #python #neural-networks #tensorflow #neural-network-algorithm #no code introduction to neural networks

1594312560

## Autonomous Driving Network (ADN) On Its Way

Talking about inspiration in the networking industry, nothing more than Autonomous Driving Network (ADN). You may hear about this and wondering what this is about, and does it have anything to do with autonomous driving vehicles? Your guess is right; the ADN concept is derived from or inspired by the rapid development of the autonomous driving car in recent years.

Driverless Car of the Future, the advertisement for “America’s Electric Light and Power Companies,” Saturday Evening Post, the 1950s.

The vision of autonomous driving has been around for more than 70 years. But engineers continuously make attempts to achieve the idea without too much success. The concept stayed as a fiction for a long time. In 2004, the US Defense Advanced Research Projects Administration (DARPA) organized the Grand Challenge for autonomous vehicles for teams to compete for the grand prize of \$1 million. I remembered watching TV and saw those competing vehicles, behaved like driven by drunk man, had a really tough time to drive by itself. I thought that autonomous driving vision would still have a long way to go. To my surprise, the next year, 2005, Stanford University’s vehicles autonomously drove 131 miles in California’s Mojave desert without a scratch and took the \$1 million Grand Challenge prize. How was that possible? Later I learned that the secret ingredient to make this possible was using the latest ML (Machine Learning) enabled AI (Artificial Intelligent ) technology.

Since then, AI technologies advanced rapidly and been implemented in all verticals. Around the 2016 time frame, the concept of Autonomous Driving Network started to emerge by combining AI and network to achieve network operational autonomy. The automation concept is nothing new in the networking industry; network operations are continually being automated here and there. But this time, ADN is beyond automating mundane tasks; it reaches a whole new level. With the help of AI technologies and other critical ingredients advancement like SDN (Software Defined Network), autonomous networking has a great chance from a vision to future reality.

In this article, we will examine some critical components of the ADN, current landscape, and factors that are important for ADN to be a success.

# The Vision

At the current stage, there are different terminologies to describe ADN vision by various organizations.

Even though slightly different terminologies, the industry is moving towards some common terms and consensus called autonomous networks, e.g. TMF, ETSI, ITU-T, GSMA. The core vision includes business and network aspects. The autonomous network delivers the “hyper-loop” from business requirements all the way to network and device layers.

On the network layer, it contains the below critical aspects:

• Intent-Driven: Understand the operator’s business intent and automatically translate it into necessary network operations. The operation can be a one-time operation like disconnect a connection service or continuous operations like maintaining a specified SLA (Service Level Agreement) at the all-time.
• **Self-Discover: **Automatically discover hardware/software changes in the network and populate the changes to the necessary subsystems to maintain always-sync state.
• **Self-Config/Self-Organize: **Whenever network changes happen, automatically configure corresponding hardware/software parameters such that the network is at the pre-defined target states.
• **Self-Monitor: **Constantly monitor networks/services operation states and health conditions automatically.
• Auto-Detect: Detect network faults, abnormalities, and intrusions automatically.
• **Self-Diagnose: **Automatically conduct an inference process to figure out the root causes of issues.
• **Self-Healing: **Automatically take necessary actions to address issues and bring the networks/services back to the desired state.
• **Self-Report: **Automatically communicate with its environment and exchange necessary information.
• Automated common operational scenarios: Automatically perform operations like network planning, customer and service onboarding, network change management.

On top of those, these capabilities need to be across multiple services, multiple domains, and the entire lifecycle(TMF, 2019).

No doubt, this is the most ambitious goal that the networking industry has ever aimed at. It has been described as the “end-state” and“ultimate goal” of networking evolution. This is not just a vision on PPT, the networking industry already on the move toward the goal.

David Wang, Huawei’s Executive Director of the Board and President of Products & Solutions, said in his 2018 Ultra-Broadband Forum(UBBF) keynote speech. (David W. 2018):

“In a fully connected and intelligent era, autonomous driving is becoming a reality. Industries like automotive, aerospace, and manufacturing are modernizing and renewing themselves by introducing autonomous technologies. However, the telecom sector is facing a major structural problem: Networks are growing year by year, but OPEX is growing faster than revenue. What’s more, it takes 100 times more effort for telecom operators to maintain their networks than OTT players. Therefore, it’s imperative that telecom operators build autonomous driving networks.”

Juniper CEO Rami Rahim said in his keynote at the company’s virtual AI event: (CRN, 2020)

“The goal now is a self-driving network. The call to action is to embrace the change. We can all benefit from putting more time into higher-layer activities, like keeping distributors out of the business. The future, I truly believe, is about getting the network out of the way. It is time for the infrastructure to take a back seat to the self-driving network.”

# Is This Vision Achievable?

If you asked me this question 15 years ago, my answer would be “no chance” as I could not imagine an autonomous driving vehicle was possible then. But now, the vision is not far-fetch anymore not only because of ML/AI technology rapid advancement but other key building blocks are made significant progress, just name a few key building blocks:

• software-defined networking (SDN) control
• industry-standard models and open APIs
• Real-time analytics/telemetry
• big data processing
• cross-domain orchestration
• programmable infrastructure
• cloud-native virtualized network functions (VNF)
• DevOps agile development process
• intelligent process automation
• edge computing
• cloud infrastructure
• programing paradigm suitable for building an autonomous system . i.e., teleo-reactive programs, which is a set of reactive rules that continuously sense the environment and trigger actions whose continuous execution eventually leads the system to satisfy a goal. (Nils Nilsson, 1996)
• open-source solutions

#network-automation #autonomous-network #ai-in-network #self-driving-network #neural-networks

1626106680

## Neural networks forward propagation deep dive 102

Forward propagation is an important part of neural networks. Its not as hard as it sounds ;-)

This is part 2 in my series on neural networks. You are welcome to start at part 1 or skip to part 5 if you just want the code.

So, to perform gradient descent or cost optimisation, we need to write a cost function which performs:

In figure 1, we can see our network diagram with much of the details removed. We will focus on one unit in level 2 and one unit in level 3. This understanding can then be copied to all units. (ps. one unit is one of the circles below)

Our goal in forward prop is to calculate A1, Z2, A2, Z3 & A3

Just so we can visualise the X features, see figure 2 and for some more info on the data, see part 1.

## Initial weights (thetas)

As it turns out, this is quite an important topic for gradient descent. If you have not dealt with gradient descent, then check this article first. We can see above that we need 2 sets of weights. (signified by ø). We often still calls these weights theta and they mean the same thing.

We need one set of thetas for level 2 and a 2nd set for level 3. Each theta is a matrix and is size(L) * size(L-1). Thus for above:

• Theta1 = 6x4 matrix

• Theta2 = 7x7 matrix

We have to now guess at which initial thetas should be our starting point. Here, epsilon comes to the rescue and below is the matlab code to easily generate some random small numbers for our initial weights.

``````function weights = initializeWeights(inSize, outSize)
epsilon = 0.12;
weights = rand(outSize, 1 + inSize) * 2 * epsilon - epsilon;
end
``````

After running above function with our sizes for each theta as mentioned above, we will get some good small random initial values as in figure 3

. For figure 1 above, the weights we mention would refer to rows 1 in below matrix’s.

Now, that we have our initial weights, we can go ahead and run gradient descent. However, this needs a cost function to help calculate the cost and gradients as it goes along. Before we can calculate the costs, we need to perform forward propagation to calculate our A1, Z2, A2, Z3 and A3 as per figure 1.

#machine-learning #machine-intelligence #neural-network-algorithm #neural-networks #networks

1596825840

## A Comparative Analysis of Recurrent Neural Networks

Recurrent neural networks, also known as RNNs, are a class of neural networks that allow previous outputs to be used as inputs while having hidden states. RNN models are mostly used in the fields of natural language processing and speech recognition.

The vanishing and exploding gradient phenomena are often encountered in the context of RNNs. The reason why they happen is that it is difficult to capture long term dependencies because of multiplicative gradient that can be exponentially decreasing/increasing with respect to the number of layers.

Gated Recurrent Unit (GRU) and Long Short-Term Memory units (LSTM) deal with the vanishing gradient problem encountered by traditional RNNs, with LSTM being a generalization of GRU.

1D Convolution_ layer_ creates a convolution kernel that is convolved with the layer input over a single spatial (or temporal) dimension to produce a tensor of outputs. It is very effective for deriving features from a fixed-length segment of the overall dataset. A 1D CNN works well for natural language processing (NLP).

## DATASET: IMDb Movie Review

TensorFlow Datasets is a collection of datasets ready to use, with TensorFlow or other Python ML frameworks, such as Jax. All datasets are exposed as `[_tf.data.Datasets_](https://www.tensorflow.org/api_docs/python/tf/data/Dataset)`, enabling easy-to-use and high-performance input pipelines.

“imdb_reviews”

This is a dataset for binary sentiment classification containing substantially more data than previous benchmark datasets. It provides a set of 25,000 highly polar movie reviews for training, and 25,000 for testing.

## Import Libraries

``````import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
``````

``````import tensorflow as tf
import tensorflow_datasets

imdb
``````

``````info
``````

## Training and Testing Data

``````train_data, test_data=imdb['train'], imdb['test']

training_sentences=[]
training_label=[]
testing_sentences=[]
testing_label=[]
for s,l in train_data:
training_sentences.append(str(s.numpy()))
training_label.append(l.numpy())
for s,l in test_data:
testing_sentences.append(str(s.numpy()))
testing_label.append(l.numpy())
training_label_final=np.array(training_label)
testing_label_final=np.array(testing_label)
``````

``````vocab_size=10000
embedding_dim=16
max_length=120
trunc_type='post'
oov_tok='<oov>'
from tensorflow.keras.preprocessing.text import Tokenizer
tokenizer= Tokenizer(num_words=vocab_size, oov_token=oov_tok)
tokenizer.fit_on_texts(training_sentences)
word_index=tokenizer.word_index
sequences=tokenizer.texts_to_sequences(training_sentences)